基于刚性检测的电力电子系统自适应仿真算法

An Adaptive Simulation Method for Power Electronics Systems Based on Stiffness Detection

高性能仿真工具对电力电子系统的设计分析具有重要的支撑作用,而考虑杂散参数对装置可靠性的影响、实施参数扫描来辅助优化设计是目前仿真应用的重要趋势。但是,考虑杂散参数后,系统的数学性质更加复杂多变,可能在刚性和非刚性之间发生转变,此时仅使用单一的前向或者后向算法都不能达到最优仿真效率,给仿真解算带来挑战。离散状态事件驱动(DSED)仿真框架可以实现对电力电子系统的准确高效解算,相较于商业仿真软件具有明显优势。但现有的DSED框架无法对系统的数学性质进行自动识别,应对上述复杂场景时仿真效率仍然有较大提升空间。为此,该文深入分析不同数值算法的效率最优场景,提出一种自适应的数值算法切换策略。该方法构造一种额外计算成本较小的判据,实现对系统刚性程度的自动检测以及不同数值积分算法的平滑切换,在仿真全过程中始终选择更优的积分方法,从而提升整体求解效率。所提策略应用于一台10 kV-2 MW四端口电力电子变压器的高频振荡现象分析中,在同等精度的前提下,仿真总体速度相较于原有DSED仿真框架提升了约4倍,进而验证了所提方法的准确性和有效性。

The high-efficiency simulation tool plays an important role in designing and analyzing power electronics systems.Meanwhile,modeling the parasitic elements to analyze their influences on system reliability and performing parameter sweep for optimal design have become trends in practical applications.However,the mathematical properties of the system can become complicated and may alternate between being stiff or non-stiff.In this situation,using a single forward or backward integration method cannot achieve the highest efficiency,which brings great challenges for simulation tools.A recently developed discrete-state event-driven(DSED)framework can achieve accurate and efficient simulation of power electronics systems and has shown great advantages over commercial software.However,it cannot automatically identify the mathematical properties of the system,so much space remains for improvement when dealing with complex simulation scenarios.This paper proposes an adaptive simulation method for power electronics systems based on stiffness detection.It can always select the better numerical solver during the simulation process with low extra cost,greatly improving the simulation efficiency.Firstly,the optimal scenarios of different numerical algorithms in power electronics system simulation are analyzed.This paper points out that only when the step size is limited by the stability rather than the accuracy of the numerical method,the stiffness of the system will bring extra difficulty for simulation.Therefore,whenever the switching event happens in power electronics systems,the high-order explicit numerical method with high accuracy should be chosen as the initial solver.After the free responses have decayed to the steady state,the low-order implicit numerical method with a large stability region should be selected.Secondly,the criterion to detect stiffness and automatically switch between different methods is constructed.The flexible-adaptive discrete-state(FA-DS)method under the DSED framework is chosen as the solver for non-stiff situations.It is a single-step variable-order variable-step method.The backward discrete-state event-driven(BDSED)method is chosen as the solver for stiff situations.It is based on the backward difference formula(BDF),a multi-step variable-order variable-step method.The adaptive solver uses the FA-DS solver as the initial solver after each switching event.Only when the order of the FA-DS solver has reached the highest order and the following calculation point is far away from the next discrete switching event,the detection will be started.Then,the adaptive solver estimates the maximum possible step size of the BDSED using the historical values and the Newton interpolation formula.If it is larger than the current step size,the BDSED solver will be used in the remaining interval until the next switching event.The computational cost of the detection is very low compared with the numerical integration process.Thus,the proposed method can always find the optimal solver to improve the overall simulation efficiency without much extra cost.The proposed method analyzes the high-frequency voltage oscillations in a 10 kV-2 MW four-port power electronics transformer.The adaptive solver is implemented under the DSED framework.The simulation results are compared with those by commercial software,the DSED framework with a single FA-DS solver and the DSED framework with a single BDSED solver.With the same level of accuracy,it achieves about 4-fold speed-up,which confirms its accuracy and efficiency.